On deferred-statistical convergence of uncertain fuzzy sequences

Abstract

Uncertain theory which was initially introduced by Liu [2016. Unceratinty Theory. 5th ed. Berlin: Springer-Verlag] is significantly speared in various fields of engineering and scientific computing such as probability theory, statistics, fuzzy set theory, measure theory, summability theories, etc. As a part of this theory, the problems of convergence with different perspectives such as the idea of convergence in distribution, in mean and in measure along with the convergence uniformly almost surely of the sequence of complex numbers have been studied using uncertain variables. Later on, the results analogue to statistical convergence have been generalized and studied by Tripathy and Nath [2017. “Statistical Convergence of Complex Uncertain Sequences.” New Mathematics and Natural Computation 13 (3): 359–374.]. In this paper, we indent to extend the investigation for the sequences of fuzzy numbers and study the uncertainty of the above ideas of convergence via deferred Cesàro mean. Certain results on deferred-statistical convergence of order for real uncertain sequences are established.